Calculating partition coefficients of small molecules in octanol/water and cyclohexane/water Caitlin C. Bannan,y Gaetano Calabró,z Daisy Y. Kyu,z and David L. Mobley∗,z,y yDepartment of Chemistry, University of California, Irvine zDepartment of Pharmaceutical Sciences, University of California, Irvine E-mail: [email protected] Phone: 949-824-6383 Abstract Partition coefficients describe how a solute is distributed between two immiscible solvents. They are used in drug design as a measure of a solute’s hydrophobicity and a proxy for its membrane permeability. We calculate partition coefficients from transfer free energies using molecular dynamics simulations in explicit solvent. Setup is done by our new Solvation Toolkit which automates the process of creating input files for any combination of solutes and solvents for many popular molecular dynamics software packages. We calculate partition coefficients between octanol/water and cy- clohexane/water with the Generalized AMBER Force Field (GAFF) and the Dielectric Corrected GAFF (GAFF-DC). With similar methods in the past we found a root-mean- squared error (RMSE) of 6.3 kJ/mol in hydration free energies which would correspond to an error of around 1.6 log units in partition coefficients if solvation free energies in both solvents were estimated with comparable accuracy. Here we find an overall 1 RMSE of about 1.2 log units with both force fields. Results from GAFF and GAFF- DC seem to exhibit systematic biases in opposite directions with GAFF and GAFF-DC for calculated cyclohexane/water partition coefficients. Introduction Partition coefficients provide a way to test the accuracy of atomistic force fields in various solvent environments. They describe the ratio of concentrations of a neutral solute molecule in a system with two immiscible solvents: [solute] P = Organic (1) [solute]Aqueous where solute refers to the neutral solute in both solvents and are typically reported as the logarithm of this concentration ratio (log P ).1–3 This differs from a distribution coefficient or “apparent partition coefficient” which includes all ionized and unionized forms of the solute.4 log P is proportional to the transfer free energy between the two solvents and can be related to the solvation free energies. Solvation free energies have been used to benchmark5–14 and inform changes15–17 to atomistic force fields, including the GROMOS 53A5 force field, which was parameterized in part using solvation free enthalpies in cyclohexane.18 However, solvation free energies can be difficult to measure experimentally10 compared to partition coefficients, which are relatively easy to measure and are measured routinely.19 The access to experimental log P values and their straightforward relationship to the solvation free energy makes partition coefficients an excellent property to test and improve the accuracy of atomistic force fields in different solvent environments. Due to the popularity of these values in the pharmaceutical industry, many tools al- ready exist to predict partition coefficients between octanol and water (log Poct). Partition coefficients are used in the pharmaceutical industry to estimate how a drug may transfer between different biological environments4,20 and are regularly used to predict a molecule’s 2 hydrophobicity.21 Additionally, many quantitative structure activity relationship (QSAR) 19 methods use calculated log Poct as an input parameter. Methods for estimating partition- ing are often based on additivity principles; for example, in 1964, Fujita et al. predicted log Poct by determining the change in the partition coefficient when a functional group was added to a benzene, then using these functional group contributions to predict partition coefficients for new compounds.22 Similar methods are still used today, where partition coef- ficients are calculated from contributions determined by molecular fragments2,23–29 or atom types, characterized by element and bonding order.30–36 In recent years, machine learning techniques have been developed using physical properties of the solute as parameters to 19,37–47 predict log Poct. However, very little work has been done to extend these methods to other organic solvents, so there are only a few examples of empirically trained methods for predicting cyclohexane/water partition coefficients.48–51 These methods vary in accuracy and efficiency, but are all trained on experimental data, meaning that they have a limited do- main of applicability. To some extent, more physical methods would be preferable, as these could be general enough to cover any organic solute-solvent combination, even combinations well outside the range of training data. One example of a relatively more physical approach is COSMO-RS, which predicts solvation and partitioning with a quantum mechanics-based approach combined with a variety of empirically-derived correction factors.5,52,53 Organic ΔGsolvation Gas ΔGtransfer ΔGhydration Aqueous Figure 1: Alchemical thermodynamic cycle used to calculate transfer free energies from solvation free energies. Here we calculate ∆GT ransfer from the difference in ∆Gsolvation into cyclohexane or octanol and ∆Ghydration. log P is directly proportional to ∆GT ransfer. 3 Here we take a physical approach to calculating partition coefficients from solvation free energies in octanol/water (log Poct) and cyclohexane/water (log Pcyc) using alchemical methods to calculate the transfer free energy. Alchemical free energy calculations take a system through computationally accessible thermodynamic pathways to connect the target end states54,55 – in this case, taking the solute out of one solvent and into the other. As discussed elsewhere, the logarithm of the partition coefficient is proportional to the transfer free energy between solvents,56 which means that we can use standard free energy techniques to compute partition coefficients via an appropriate combination of solvation free energy calculations. Specifically, we calculate the transfer free energy as the difference between the hydration free energy and the solvation free energy into the organic phase (Figure 1). Similar methods for calculating hydration free energies have yielded fairly accurate results.,6,11,13,14 as did a recent effort for predicting relative solubilities in a variety of organic solvents this approach.57 A variety of previous studies have calculated partition coefficients from solvation free energies. Early attempts to calculate log P based molecular dynamics simulations used free energy perturbation, changing the identity of the solute in both solvents to obtain octanol/water56,58 and chloroform/water59–61 relative partition coefficients (comparing par- tition of two different solutes). A number of attempts have been made to calculate log P from absolute solvation free energies with all atom force fields.16,62–64 For example, two recent stud- ies used a hydrid atomic level/coarse grained force field with the General AMBER Force Field (GAFF)65 for solute parameters.,66,67 the same force field we apply here. Our present study is the first attempt at log P calculations with the Dielectric Corrected General AMBER Force Field (GAFF-DC)15 for such calculations, and we are not aware of any prior applications of alchemical techniques to the calculation of water-cyclohexane partition coefficients other than the relative work using free energy perturbation noted above. Another new feature of this work is that we provide an automated work flow for solvation free energies and therefore partition coefficient calculations, in that our new Solvation Toolkit was used to create all 4 input files and is available on GitHub at https://github.com/MobleyLab/SolvationToolkit, and analysis of the solvation free energies was fully automated with the Alchemical Analysis tool.68 To facilitate additional applications of this technique, all setup and analysis scripts are also available in the Additional information, which is provided free on charge online at http://n2t.net/ark:/b7280/d15k5m Computational Theory and Methods Automated setup for arbitrary mixtures using Solvation Toolkit Molecular modeling in different software packages requires a variety of input file types, termi- nal applications, and work flows. In an effort to automate our simulations, we have created Solvation Toolkit to generalize workflows across different software packages. It aims to de- liver a simple tool to set mixtures of arbitrary combinations of solutes and solvents for use in popular molecular dynamics software packages such as GROMACS69–75 and AMBER This piece of software relies on other software packages including OpenMolTools,76,77 OpenEye’s Python toolkits,78–88 AmberTools,89–94 Packmol,95 ParmEd,96 and MDTraj.97 The program can be logically divided into three main sections related to different tasks: converting simple input to molecular structures, generating force field parameters, and build- ing a solvated box. These are followed by output to the proper file formats. The toolkit begins by requiring the IUPAC name or the SMILES string and the desired number of molecules for all compounds in the system. As recommended by OpenEye,98 the OEChem toolkit is used to convert these into a molecular structure and generate up to 800 confor- mations of the molecule. Next, the Quacpac toolkit is used to automatically select the best conformation and to assign symmetric AM1-BCC charges.88,99 OpenEye’s toolkits were used rather than Antechamber as OpenEye’s AM1-BCC implementation is maintained by Christopher Bayly, one of the original authors of AM1-BCC, and has several features beyond Antechamber’s AM1-BCC, including better handling of multi-conformer molecules, proper 5 symmetrization of charges which ought to be symmetric, and others.98 Using AMBER mod- ules, GAFF parameters are assigned to the charged molecule with Antechamber and LEaP is used to produce a monomer topology file. Then the monomers for each compound in the mixture are assembled using Packmol to pack the different types of molecules into a box region defined by geometric constraints to keep atoms from different molecules at a safe pairwise distance.95 Finally, LEaP is used to generate the final AMBER topology and coor- dinate files of the solvated mixture.